I've read that the eye color at birth for most humans and for cats may not always be the the true genetic color at first. This is due to the lack of melanin in the iris. This makes sense as there is no light in the womb to stimulate the production of melanin.

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The blue colour is an example of structural colour, caused by light interacting physically with something. Some examples of structural colour are the iridescence of insect wings and body surfaces (usually caused by repeating chitinous structures), and of certain birds feathers, as well as the non-iridescent colours of the blue and yellow macaw.

In the case of the eye it is the stroma of the iris that is responsible. This is a network of fibrous tissue which scatters light. When light is scattered in this way (Rayleigh scattering) it is the short wavelengths which are most scattered. So when you look at the sky (away from the sun) you are seeing diffuse blue light created by this scattering in the atmosphere. In the case of the iris what you are seeing is light reflected from the eye being scattered within the iris, creating the diffuse blue colour. As you say in the question, everything else is down to melanin.

The generation of iris color is quite complex and the exact color of the eyes depends upon many different factors, not just melanin. In fact, blue coloration does not depend on a specific chemical, but on the structure of the eye itself.

In the brown iris there is an abundance of melanocytes and melanin in the anterior border layer and stroma whereas in the blue iris these layers contain very little melanin. As light traverses these relatively melanin-free layers, collagen fibrils of the iris scatter the short blue wavelengths to the surface, thus a blue iris is a consequence of structure not of major differences in chemical composition. Different shades of blue, and in irises with a limited amount of melanin, different shades of grey, green and hazel, are determined
by the thickness and density of the iris itself and the extent of accumulation of white collagen fibres, as well as patches of tissue loss in the anterior border layer and stroma.
However, a careful examination of people’s irises makes it clear that there are characteristics other than eye colour that present in the human iris. The iris has been analysed to show that it can display a degree of complexity encompassing over 240 degrees of freedom (Daugman, 2003).